Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C13×D8 | C2 | semidirect |
| 2. C2×#88066 | C2 | semidirect |
| 3. #11718356 | C2 | semidirect |
| 4. #11718083 | C2 | semidirect |
| 5. C4⋊#6090 | C2 | semidirect |
| 22. C13×D8 | D4 | semidirect |
| 51. C4×D8 | D13 | semidirect |
| 63. C4×C13 | D16 | semidirect |
| 90. D8 | D52 | semidirect |
| 97. C13 | #2206 | semidirect |
| 123. C4 | #88066 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×D8 | 2 |
| C2×#88066 | 2 |
| #11718356 | 2 |
| #11718083 | 2 |
| C4⋊#6090 | 2 |
| #2206 | 13 |